Reichel (2025) defined the bariance as a pairwise-difference measure that can be rewritten in linear time using only scalar sums. We extend this idea to the covariance matrix by showing that the standard matrix expression involving the uncentered Gram matrix and a correction term is algebraically identical to the pairwise-difference definition while avoiding explicit centering. The computation then reduces to one outer product of dimension p-by-p and a single subtraction. Benchmarks in Python show clear runtime gains, especially when BLAS optimizations are absent. Optionally faster Gram-matrix routines such as RXTX (Rybin et al., 2025) further reduce overall cost.

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct implementations, particularly on SO(3), are error-prone due to issues such as axis conventions, normalizations, composition consistency and subtle errors that only appear in edge cases. SciPy's spatial$.$transform module is a rigorously tested Python implementation. However, it historically only supported NumPy, limiting adoption in GPU-accelerated and autodiff-based workflows. We present a complete overhaul of SciPy's spatial$.$transform functionality that makes it compatible with any array library implementing the Python array API, including JAX, PyTorch, and CuPy. The revised implementation preserves the established SciPy interface while enabling GPU/TPU execution, JIT compilation, vectorized batching, and differentiation via native autodiff of the chosen backend. We demonstrate how this foundation supports differentiable scientific computing through two case studies: (i) scalability of 3D transforms and rotations and (ii) a JAX drone simulation that leverages SciPy's Rotation for accurate integration of rotational dynamics. Our contributions have been merged into SciPy main and will ship in the next release, providing a framework-agnostic, production-grade basis for 3D spatial math in differentiable systems and ML.

Tangent is the first AD framework using SCT in a dynamically typed language.

Tangent is the first AD framework using SCT in a dynamically typed language.

Broadly, we expect slowdowns to be attributed to one of the following categories: 1.

Optimizing the performance of large-scale software repositories demands expertise in code reasoning and software engineering (SWE) to reduce runtime while preserving program correctness. However, most benchmarks emphasize what to fix rather than how to fix code. We introduce SWE-fficiency, a benchmark for evaluating repository-level performance optimization on real workloads. Our suite contains 498 tasks across nine widely used data-science, machine-learning, and HPC repositories (e.g., numpy, pandas, scipy): given a complete codebase and a slow workload, an agent must investigate code semantics, localize bottlenecks and relevant tests, and produce a patch that matches or exceeds expert speedup while passing the same unit tests. To enable this how-to-fix evaluation, our automated pipeline scrapes GitHub pull requests for performance-improving edits, combining keyword filtering, static analysis, coverage tooling, and execution validation to both confirm expert speedup baselines and identify relevant repository unit tests. Empirical evaluation of state-of-the-art agents reveals significant underperformance. On average, agents achieve less than 0.15x the expert speedup: agents struggle in localizing optimization opportunities, reasoning about execution across functions, and maintaining correctness in proposed edits. We release the benchmark and accompanying data pipeline to facilitate research on automated performance engineering and long-horizon software reasoning.

Property-based testing (PBT) is a lightweight formal method, typically implemented as a randomized testing framework. Users specify the input domain for their test using combinators supplied by the PBT framework, and the expected properties or invariants as a unit-test function. The framework then searches for a counterexample, e.g. by generating inputs and calling the test function. In this work, we demonstrate an LLM-based agent which analyzes Python modules, infers function-specific and cross-function properties from code and documentation, synthesizes and executes PBTs, reflects on outputs of these tests to confirm true bugs, and finally outputs actionable bug reports for the developer. We perform an extensive evaluation of our agent across 100 popular Python packages. Of the bug reports generated by the agent, we found after manual review that 56\% were valid bugs and 32\% were valid bugs that we would report to maintainers. We then developed a ranking rubric to surface high-priority valid bugs to developers, and found that of the 21 top-scoring bugs, 86\% were valid and 81\% we would report. The bugs span diverse failure modes from serialization failures to numerical precision errors to flawed cache implementations. We reported 5 bugs, 4 with patches, including to NumPy and cloud computing SDKs, with 3 patches merged successfully. Our results suggest that LLMs with PBT provides a rigorous and scalable method for autonomously testing software. Our code and artifacts are available at: https://github.com/mmaaz-git/agentic-pbt.

We introduce a benchmark framework developed by and for the scientific community to evaluate, monitor and steer large language model development in fundamental physics. Building on philosophical concepts of scientific understanding and creativity, we develop a scoring system in which each question is scored by an expert for its correctness, difficulty, and surprise. The questions are of three forms: (i) multiple-choice questions for conceptual understanding, (ii) analytical problems requiring mathematical derivation, and (iii) openended tasks requiring complex problem solving. Our current dataset contains diverse set of examples, including a machine learning challenge to classify high-energy physics events, such as the four top quark signal. To ensure continued relevance, we propose a living benchmark, where physicists contribute questions, for instance alongside new publications. We invite contributions via: http://www.physicsbenchmarks.org/. We hope that this benchmark will enable a targeted AI development that can make a meaningful contribution to fundamental physics research.

The rapid evolution of software libraries poses a considerable hurdle for code generation, necessitating continuous adaptation to frequent version updates while preserving backward compatibility. While existing code evolution benchmarks provide valuable insights, they typically lack execution-based evaluation for generating code compliant with specific library versions. To address this, we introduce GitChameleon 2.0, a novel, meticulously curated dataset comprising 328 Python code completion problems, each conditioned on specific library versions and accompanied by executable unit tests. GitChameleon 2.0 rigorously evaluates the capacity of contemporary large language models (LLMs), LLM-powered agents, code assistants, and RAG systems to perform version-conditioned code generation that demonstrates functional accuracy through execution. Our extensive evaluations indicate that state-of-the-art systems encounter significant challenges with this task; enterprise models achieving baseline success rates in the 48-51% range, underscoring the intricacy of the problem. By offering an execution-based benchmark emphasizing the dynamic nature of code libraries, GitChameleon 2.0 enables a clearer understanding of this challenge and helps guide the development of more adaptable and dependable AI code generation methods. We make the dataset and evaluation code publicly available at https://github.com/mrcabbage972/GitChameleonBenchmark.